Self-adjointness of the semi-relativistic Pauli-Fierz Hamiltonian

Takeru Hidaka; Fumio Hiroshima

doi:10.1142/S0129055X15500154

Self-adjointness of the semi-relativistic Pauli-Fierz Hamiltonian

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Abstract

The spinless semi-relativistic Pauli-Fierz Hamiltonian H= (p o×1-A)²+M²+Vo× 1+1o×H_f, in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, H_f the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli-Fierz model with a fixed total momentum P ε^d: H(P) = s(P P _f - A(0))² + M² + H_f, M ≥ 0 is also proven for arbitrary P.

Original language	English
Article number	1550015
Journal	Reviews in Mathematical Physics
Volume	27
Issue number	7
DOIs	https://doi.org/10.1142/S0129055X15500154
Publication status	Published - Aug 19 2015

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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title = "Self-adjointness of the semi-relativistic Pauli-Fierz Hamiltonian",

abstract = "The spinless semi-relativistic Pauli-Fierz Hamiltonian H= (p o×1-A)2+M2+Vo× 1+1o×Hf, in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hf the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli-Fierz model with a fixed total momentum P εd: H(P) = s(P P f - A(0))2 + M2 + Hf, M ≥ 0 is also proven for arbitrary P.",

author = "Takeru Hidaka and Fumio Hiroshima",

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T1 - Self-adjointness of the semi-relativistic Pauli-Fierz Hamiltonian

AU - Hidaka, Takeru

AU - Hiroshima, Fumio

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Y1 - 2015/8/19

N2 - The spinless semi-relativistic Pauli-Fierz Hamiltonian H= (p o×1-A)2+M2+Vo× 1+1o×Hf, in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hf the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli-Fierz model with a fixed total momentum P εd: H(P) = s(P P f - A(0))2 + M2 + Hf, M ≥ 0 is also proven for arbitrary P.

AB - The spinless semi-relativistic Pauli-Fierz Hamiltonian H= (p o×1-A)2+M2+Vo× 1+1o×Hf, in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hf the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli-Fierz model with a fixed total momentum P εd: H(P) = s(P P f - A(0))2 + M2 + Hf, M ≥ 0 is also proven for arbitrary P.

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Self-adjointness of the semi-relativistic Pauli-Fierz Hamiltonian

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